Sparse Gaussian Processes with Uncertain Inputs for Multi-Step Ahead Prediction

Multi-step ahead prediction is a common approach for the simulation of dynamic system behavior. Recently, Gaussian Processes combined with an autoregressive model structure gathered much attention for this task. In order to overcome the computational burden of standard Gaussian Processes at large data sets and to provide a reliable variance prediction for time-dependent use cases, we introduce in the present paper the combination of several sparse Gaussian Process approximations with the framework of uncertainty propagation. We show the results of the proposed approaches at an artificial, chaotic time series and a real world example stemming from an engine air system. The real world example also contains a comparison of the modeling performance to other data-based methods, in particular ordinary least squares and multi-layer perceptrons.